22 Communication Systems CHAPTER 2 Amplitude and Angle Modulation 2.1 INTRODUCTION Modulation is the process or result of the process by which a message is changed into information. Modulation plays vital role in the field of communication. Communication involves the transmission, reception and processing of information by electrical means. For the propagation of electric signals, the media used is electromagnetic field and when this field changes with time it takes the form of wave. Modulation is also the process whereby in response to the received wave either the original message or information pertaining the original message is made available in the desired form and is delivered when it is wanted. “Demodulation and detection” are the terms often observed to denote the recovery of the wanted message from a modulated signal. Modulation is fundamental to communication and it implies the bandwidth occupancy. In the chapter, we will basically deal with the fundamental concepts of Amplitude Modulation and Phase Modulation. 2.2 NEED FOR MODULATION If the signal is send directly, i.e. without modulation, i.e. unmodulated carrier several difficulties arise which are listed below: (1) Antenna height: Theory of antenna tells that for the efficient radiation of electromagnetic waves the height of antenna must be comparable to the quarter wavelength of the frequency which we are using. Now suppose you want to transmit the audio frequency, i.e. 20 kHz, we know that Cf= λ C ∴λ = (1) f where, λ = wavelength, C = velocity of light, f = frequency 24 Communication Systems In the process of modulation low frequency bandlimited signal is mixed with high frequency wave called, “carrier wave”. Such a carrier wave may be represented by the equation e = Em sin (ωt + φ) (2) where, e = instantaneous value of sine wave, Em = maximum amplitude, ω = angular frequency, φ = phase relation with respect to some reference. Any of these last three characteristics or parameters of the carrier may be varied by the low frequency modulating signal during the process of modulation. Thus, in the process of modulation, some characteristics of high frequency sinusoidal wave is varied in accordance with the instantaneous value of modulating signal since there are three parameters Em, ω and φ of a carrier wave, therefore, any of these parameters can be varied in proportion to the instantaneous value of the modulating signal, giving rise to amplitude, frequency or phase modulation respectively. Frequency and phase modulation are together named as “angle modulation”, as variation of any of the two varies the angle of the carrier wave. Amplitude Modulation: In this type of modulation, the amplitude of carrier signal is varied by the modulating voltage, whose frequency is less than that of carrier. Let Vc = Vc sin ωc t and Vm = Vm sin ωm t in the above expressions, the phase angle has been ignored. 2.3 FREQUENCY SPECTRUM OF AM WAVE Amplitude modulation is a system of modulation in which the amplitude of the carrier is made proportional to the instantaneous amplitude of modulating signal. Sideband frequency is defined as fSB = fc ± n fm (3) and in the first pair n = 1. When a carrier is amplitude modulated, the proportionality constant is made equal to unity and the instantaneous modulating voltage variations are superimposed on to the carrier amplitude. Hence, when there is no modulation, the amplitude of carrier is equal to its unmodulated value. When modulation is present the amplitude of the carrier is varied by its instantaneous value. This is shown in Fig. 2.1. In the figure it is clear that what will happen if Em is greater than Ec. Modulation index (m) is given by Em m = (4) Ec 26 Communication Systems mE E= E sin ω t +c [cos( ω −ω )t − cos( ω +ω )t] cc2 cm cm mEccmE E=ω+ω−ω−ω+ω Ecc sin t cos(cm )t cos(cm )t (7) 22 where, Ec sin ωc t = Unmodulated carrier mEc cos(ωcm −ω )t = Lower sideband 2 mEc −cos( ωcm +ω )t = Upper sideband 2 Total additional terms produced are the two sidebands. fc – fm = Lower sideband (LSB) fc + fm = Upper sideband (USB) This important conclusion is that the bandwidth required for amplitude modulation is twice the frequency of the modulating signal. 2.4 REPRESENTATION OF AM WAVE Figure 2.2 shows frequency spectrum of AM wave. C LSB USB (fcm – f ) (fcm + f ) Fig. 2.2: Spectrum of AM Wave Here in Fig. 2.2, AM is simply shown comprising of three different frequencies. The central frequency, i.e. carrier is having the highest amplitude and other two are placed symmetrical about it. They are having equal amplitudes. They never exceed half the carrier amplitude. Amplitude modulated wave is shown in Fig. 2.3. Area of top envelope is given by Ec + Em sin ωm t Area of the bottom envelope is given by – A = – (Ec + Em sin ωm t) Amplitude and Angle Modulation 27 Ecm + E sinw m t Emax Em Ec Emin t – (Ecm + E sinw m t) Fig. 2.3: Amplitude Modulated Wave Modulated wave extends between these two limits and has repetition rate equal to modulated carrier frequency. To Find Modulation Index: Amplitude of modulated carrier varies as, A = Ec [1 + m sin ωm t] The maximum and minimum values of A are, Ec (1 + ma) & Ec (1 – ma) and are denoted as Emax & Emin respectively. Hence, Emax = Ec (1 + ma) Emin = Ec (1 – ma) EEmax− min This gives ma = (8) EEmax+ min This equation is the standard method of evaluating the modulation index when calculating from a waveform. Such as may be seen on an oscilloscope. Oscilloscope Display of AM Pattern shown in Fig. 2.3 can be obtained directly on oscilloscope and modulation index can be measured directly from this modulated waveform. (a) Modulated wave is applied to the vertical deflection circuit of oscilloscope and modulating signal to horizontal deflection circuit. Amplitude and Angle Modulation 29 Antenna (LLM) (HLM) Class C Class A Class C Class B RF RF Crystal Buffer RF O/P RF Linear Power Oscillator Ampr. ampr Power Ampr. Ampr AF AF Modulator AF AF Processing Class B AF pre & Power Class B in Ampr Filtering Ampr. O/P Ampr. Fig. 2.4: AM Transmission Block Diagram 2.6 POWER RELATION IN AM WAVE Modulated wave contains more power than the carrier had before modulation took place. Since the amplitude of the side bands depends on the modulation index, it is anticipated that the total power in the modulated wave will depend on the modulation index also. The total power in the modulated wave will be E2 EE 22 P =carrier ++ LSB USB (9) t R RR where, all three voltages are rms values & R is the resistance in which power is dissipated. 2 E carrier EE222 ∴=P carrier = =c (10) c R R 2R 2 mE c mE22 PP= = 2 /R= c LSB USB 2 8R 22 2 2 mEcc E m = = (11) 8R 2R 4 ∴ Putting values of equations (11) & (10) in equation (9) 30 Communication Systems EE22 E 2 P =++carr LSB USB t RR R EE22mm22 E 2 ∴=P cc + + c t 2R 2R 4 2R 4 EE22mm22 EE22 m2 =+cc +=+ cc 2R 2R 4 4 2R 2R 2 2 2 Ec m P1t = + 2R 2 2 Ec but P = carrier power = c 2R m2 ∴=Ptc P1 + (12) 2 Example 2.1: A broadcast AM transmitter radiates 50 kW of carrier power what will be radiated power at 85% modulation? Given Pc = 50 kW Percentage modulation = 85 To find : Pt = total power radiated. Solution: m2 Ptc= P1 + 2 (0.85)2 =50 kW 1 + 2 = 68.06 kW. Example 2.2: A broadcast radio transmitter radiates 10 kW when the modulation percentage is 60. How much of this is carrier power? Solution: Pta= 10 kW, m = 60% 32 Communication Systems ω 6.28× 107 ∴ f =c = =10 MHz c 22ππ fc = 10 MHz ω 3140 f =m = = 500 Hz (b) Modulating frequency: m 22ππ 2 2 Ec 500 (c) Carrier power: Pc = = = 208.33 W 2R 2× 600 (d) Mean power output: 2 2 ma 2500 0.4 2500 Ptc=+= P1 1 + = ×1.08 2 12 2 12 Pt = 225 watts (e) Peak power output results when the positive half cycle of the modulating signal occurs. The peak output voltage is given by the sum of Ec & Em: Peak output voltage = Ec + m Ec = 500 + 0.4 × 500 Peak output voltage = 700 V 700 700 1 Peak power==×× Ptm 22600 Ptm = 408.3 watts 2.7 CURRENT CALCULATIONS FOR AM WAVE Sometimes it is easy to measure RF currents instead of voltages. We analyze such a situation in this section. Let Ic be rms unmodulated current. It = Total rms modulated current of AM transmitter. R = Resistance in which the above two currents flow. Then, 22 Ptt IR I t =22 = Pc IRcc I 2 Pmta but =1 + P2c Amplitude and Angle Modulation 35 2.10 NON-LINEAR MODULATION In general, any device operated in non-linear region of its output characteristics is capable of producing amplitude modulated waves when the carrier and modulating signals are fed at the input. Thus, a transistor, a triode tube, a diode, etc. may be used as Square Law modulator. In such a modulator circuit, the output current flowing through the load is given by the power series 2 i = a0 + a1 e1 + a2 e1 + … where, a0, a1, a2, etc. are constant and e1 is the input voltage to the device. Considering the modulator circuit of Fig. 2.5 e1 =Ec sin ωc t + Em sin ωm t i=a0 + a1 (Ec sin ωc t + Em sin ωm t) + 2 a2 (Ec sin ωc t + Em sin ωm t) 2 2 =a0 + a1 Ec sin ωc t + a1 Em sin ωm t + a2 Ec sin ωc t 2 2 + a2 Em sin ωm t + 2 Ec Em sin ωc t sin ωm t 2 2 2 2 =a0 + a1 Ec sin ωc t + a1 Em sin ωm t + a2 Em sin ωm t + a2 Ec sin ωc t 2E a E + c2 m [cos (ω – ω ) t – cos (ω + ω ) t] 2 c m m 2 2 i=a0 + a1 Ec sin ωc t + a1 Em sin ωm t + a2 Ec sin ωc t 2 2 + a2 Em sin ωm t + a2 EcEm [cos (ωc – ωm) t – cos (ωc + ωm)t] The last term of this equation (underlined) gives the upper and lower sidebands while the second term gives the carrier.